...SIMILAR Solids, are such as are contained under the same number of similar planes, alike situated. — Similar solids are to each other as the cubes of their like linear dimensions. SIMILAR Solid Numbers, are those whose little cubes may be so ranged, as to form...

...DIAGONAL ROD. The construction of this instrument is founded upon Theo. XX, Part III.; namely, that similar solids are to each other as the cubes of their like dimensions. Hence, it appears that the original construction of the diagonal line was extremely easy...

...nearly the same as the General Rules. Its construction is founded upon Theo. 20, Part I. ; viz. that similar solids are to each other as the cubes of their like dimensions. tfote I. Those who have not a diagonal rod, may nevertheless find the content of a cask...

...determined by means of its specific gravity. But a shot, four inches in diameter, weighs 9.0029 pounds, and similar solids are to each other as the cubes of their like linear dimensions. Also, the specific gravity of gunpowder, in a closely shaken mass, is 920, — Consequently,...

...vertices of the ungulas, is = to | of the cone BDS, since the diameter of its base is necessarily = ^ that of the larger, and since they are similar solids...cone be cut by a plane perpendicular to the plane of its buse, the convex surface of the cone, and the plane of the base, will be divided in the same...

...vertices of the ungulas, is = to £ of the cone BDS, since the diameter of its base is necessarily = ^ that of the larger, and since they are similar solids...for similar solids are to each other as the cubes <>f their like sides, (Prop. XXXV, B. II, El. S. Geom.) and cube of 1 is 1, cube of 2 is 8 ; hence...

...INVOLVING THE PRINCIPLES OF THE CUBE ROOT. 121. It is an established theorem of geometry, that all similar solids are to each other as the cubes of their like dimenswns. 1. If a cannon-ball, 3 inches in diameter, weigh 8 pounds, what will a ball of the same...

...are inscribed ; or as the squares of the diameters of those circles. (Em. IV. 36.) THEOREM XX. All similar solids are to each other, as the cubes of their like dimensions. (Em. VI. 24.) PART THE SECOND. A DESCRIPTION OF THE CHAIN, CROSS-STAFF, OFFSETSTAFF, COMPASS,...

...EXAMPLES INVOLVING THE PRINCIPLES OF THE CUBE ROOT. 79. IT is an established theorem of geometry, that all similar solids are to each other as the cubes of their like dimensions. 1. If a cannon ball 3 inches in diameter weigh 8 pounds, what will a ball of the same metal...

...cube root of the solidity of the latter. The whole truth may be thus expressed. • The contents of similar solids are to each other as the cubes of their like dimensions ; and like dimensions of similar solids are to each other as the cube roots of their contents....